David Cameron has set up a new government task force on tackling extremism and radicalisation in the wake of the Woolwich attack that left soldier Lee Rigby dead.

Downing Street said on Monday that the task force, which met for the first time today, will meet monthly from now on.

Speaking in the Commons on Monday, Cameron said the attack was "a betrayal of Islam" and the those responsible had "sought to justify their actions by an extremists ideology that perverts and warps Islam".

"There is nothing in Islam that justifies acts of terror and I welcome the spontaneous condemnation from Mosques," he told MPs.

The prime minister has asked ministers to work on "practical suggestions" which the task force could discuss at future meetings.

Education secretary Michael Gove and education minister David Laws are to to look at confronting extreme views in schools and charities, with business secretary Vince Cable looking at universities.

Justice secretary Chris Grayling will look into similar issues in prisons. And faith and communities minister Baroness Warsi will to look at work in communities.

Cameron told the Commons: "When young men born and bred in this country are radicalised and turned into killers we have to ask some tough questions.

"It is as if for some young people there is a conveyor belt to radicalisation. We need to dismantle this process."

The prime minister also said the government would not tolerate far-right groups such as the English Defence League which try to "demonise Islam and stole up anti Muslim hatred".

Speaking in the House of Lords on Monday afternoon, Baroness Warsi said there was "no religious justification for these acts" and repeated Cameron's statement that "Islam is a religion of peace".

Michael Adebolajo, one of two men charged with the brutal murder of Drummer Lee Rigby, appeared in court today and asked to be known as Mujahid Abu Hamza.

The 28-year-old, of Romford, Essex, appeared at Westminster Magistrates' Court, and was charged with the murder of the young soldier, and the attempted murder of two police officers.

Another man, 22-year-old Michael Adebowale, also has been charged with murdering Rigby, who died of "multiple incised wounds," according to a post-mortem.